You are right that the real universe is not mathematical in the absolute sense. Mathematics is not the sole language of Nature. It depicts only its quantitative aspect. You are also right that what we call rest is the net null sum of all forces acting on a body. Nothing is truly at rest in Nature. Every object is only relatively at rest on its 'ground' or 'base'. Since this aspect of reality is not evident in observation, you can describe it as abstract. But objects and interactions are real. We define reality as everything that exists (has a limited structure that evolves in time), is intelligible (perceivable or knowable as the result of measurement) and communicable (describable in a language as defined in our essay: Transposition of information to another system's CPU or mind by signals or sounds using energy. The transposition may relate to a fixed object/information. It can be used in different domains and different contexts or require modifications in prescribed manner depending upon the context).
We differentiate real from the abstract in the following manner: Space, Time and coordinates arise from our concept of sequence and interval. When it is related to objects, we call the interval space. When it is related to events, we call the interval time. When we describe inter-relationship of objects, we describe the interval by coordinates. Everything is subject to time evolution in space. There is a fixed pattern of all events. These are: being (situation leading to its creation), becoming (its creation itself), (growth due to addition of other particles/events), transformation (as a result), transmutation (due to the same effect - incompatible/excess addition), destruction (change of form as a consequence) to start a new chain. Observation/measurement (perception) is of two types. Some things can be directly observed and measured (which you call real universe). But space, time and coordinates that have no physical existence, but are only inferred from indirect observation/measurement of two successive objects or events or arrangements. This second category belongs to the realm of the abstract. Motion also belongs to this category because space, where motion takes place, is abstract. Yet, it can be measured indirectly by linking it to real objects in space. Einstein's zero commencement point belongs to the abstract coordinates. Hence it has to be linked to real objects for meaningful use.
One word of caution: mirages are also observed. But such observation is dependent on a vantage position and not invariant (falsifiable) from different positions. Thus, they are neither real nor abstract: they are only imaginary combinations of real objects which cannot be physically coupled - like complex numbers. What you call a 'zero physical state' is not zero, because zero is the absence of something that does not exist at here-now (where observation/ measurement takes place), but exists elsewhere. Absolute zero in temperature parlance is a certain temperature threshold, not zero temperature.